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Convert Area Units in Square Inches, Square Feet, and Square Yards

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In this video, we will convert customary square units. In the first example, we are asked to convert six square feet to square inches. Let’s begin by determining the conversion from square feet to square inches. Looking on the right, notice how here we have a square that is one foot by one foot, and therefore, this is one square foot, but we also know that one foot is equal to 12 inches, and therefore, this square is also 12 inches by 12 inches, and therefore, in square inches, the area of one square foot is equal to 12 inches times 12 inches, which is 144 square inches, so we now know that one square foot is equal to 144 square inches. Now to perform the conversion, let’s write six square feet as a fraction with a denominator of one, and now we’ll multiply by a unit fraction using the conversion that will convert these square feet to square inches, notice how we have square feet in the numerator, and we want square feet to simplify out, leaving us with square inches, and therefore, in the unit fraction, we need to have square feet in the denominator and square inches in the numerator, and again, since one square foot is equal to 144 square inches, the unit fraction is 144 square inches over one square foot.

And again, because we have square feet divided by square feet, the units of square feet simplify out leaving us with square inches, and now we multiply to perform the conversion. Notice the denominator is one, and therefore the product is just six times 144 square inches. Six times 144 is equal to 864. We have 864 square inches, so six square feet is equal to 164 square inches. And now for the second example, we’re asked to convert nine square yards to square feet. Let’s begin by writing nine square yards as a fraction with a denominator of one.

And now let’s determine the conversion from square yards to square feet, looking on the right, notice how here we have a square that is one yard by one yard, this is one square yard, but we also know one yard is equal to three feet, and therefore the dimensions are also three feet by three feet, and the area of a square that is three feet by three feet, is equal to three feet times three feet, which is nine square feet. We now know one square yard is equal to nine square feet, and now we’ll use this conversion to form a unit fraction to convert nine square yards to square feet.

We know we want square yards to simplify out, and since we have square yards in the numerator here, we must have square yards in the denominator and square feet in the numerator. Using the conversion, the unit fraction is nine square feet over one square yard. The units of square yards simplify out leaving us with square feet, nine times nine is 81, giving us 81 square feet. Nine square yards is equal to 81 square feet. I hope this was helpful.

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